

    \filetitle{regress}{Centred population regression for selected model variables}{model/regress}

	\paragraph{Syntax}

\begin{verbatim}
[B,CovRes,R2] = regress(M,Lhs,Rhs,...)
\end{verbatim}

\paragraph{Input arguments}

\begin{itemize}
\item
  \texttt{M} {[} model {]} - Model on whose covariance matrices the
  popolation regression will be based.
\item
  \texttt{Lhs} {[} char \textbar{} cellstr {]} - Lhs variables in the
  regression; each of the variables must be part of the state-space
  vector.
\item
  \texttt{Rhs} {[} char \textbar{} cellstr {]} - Rhs variables in the
  regression; each of the variables must be part of the state-space
  vector, or must refer to a larger lag of a transition variable present
  in the state-space vector.
\end{itemize}

\paragraph{Output arguments}

\begin{itemize}
\item
  \texttt{B} {[} namedmat \textbar{} numeric {]} - Population regression
  coefficients.
\item
  \texttt{CovRes} {[} namedmat \textbar{} numeric {]} - Covariance
  matrix of residuals from the population regression.
\item
  \texttt{R2} {[} numeric {]} - Coefficient of determination
  (R-squared).
\end{itemize}

\paragraph{Options}

\begin{itemize}
\tightlist
\item
  \texttt{\textquotesingle{}matrixFmt=\textquotesingle{}} {[}
  \emph{\texttt{\textquotesingle{}namedmat\textquotesingle{}}}
  \textbar{} \texttt{\textquotesingle{}plain\textquotesingle{}} {]} -
  Return matrices \texttt{B} and \texttt{CovRes} as either
  \href{namedmat/Contents}{\texttt{namedmat}} object (i.e.~matrices with
  named rows and columns) or plain numeric arrays.
\end{itemize}

\paragraph{Description}

Population regressions calculated by this function are always centred.
This means the regressions are always calculated as if estimated on
observations with their uncondional means (the steady-state levels)
removed from them.

The Lhs and Rhs variables that are log variables must include
\texttt{log(\ )} explicitly in their names. For instance, if \texttt{X}
is declared to be a log variable, then you must refer to \texttt{log(X)}
or \texttt{log(X\{-1\})}.

\paragraph{Example}

\begin{verbatim}
[B,C] = regress('log(R)',{'log(R{-1})','log(dP)'});
\end{verbatim}


